UC Berkeley

This dissertation investigates the design of control algorithms and calibration methods for

Microscale Rate Integrating Gyroscopes (MRIGs). As its name implies, a MRIG operates

in rate integrating mode and can directly measure the rotation angle of the base where it

is mounted. However, the MRIG mechanical system does not spontaneously operate in a

rate integrating mode, but requires an active controller. Such a controller enables the MRIG to oscillate in a specific pattern that is related to the input rotation angle in a measurable way.

Conventional micro-machined gyroscopes (i.e. MEMS gyroscopes) operate in rate mode (as apposed to rate integrating mode). That is, the gyroscope directly measures the rotation rate of the base. The measured rotation rate is then numerically integrated over time to obtain the input rotation angle. The main drawback of this measuring mechanism is that, by integrating, the rate measurement error will propagate over time, causing the angle measurement to drift from the real input angle. MRIG, by its operating principle, can directly measure the input rotation angle; hence it suffers from no such error propagation.

A well-known control scheme for rate integrating gyroscopes was proposed by Lynch in 1995 [51]. This control scheme has demonstrated its efficacy on precisely fabricated rate integrating gyroscopes such as Hemispherical Resonance Gyroscopes (HRGs). However, for MRIGs fabricated by micro-fabrication technology, fabrication imperfections significantly degrade the gyro performance. In addition, the Lynch-proposed-scheme is essentially nonlinear. As a consequence, the controller performance is hard to predict and analyze prior to real tests.

In this dissertation, a novel demodulation method is developed to transform the original nonlinear control problem into a linear time invariant controller design problem. This technique is based on the averaging method proposed by Lynch [50] but enables the use of well studied linear system theory for MRIG controller design and analysis. The resulting controller design for MRIGs is much more tractable and the performance is rather predictable. This fundamental improvement also opens up new opportunities for implementing and analyzing control systems based on linear control theory.

Two schemes are proposed in this dissertation to compensate for the parameter mismatches caused by fabrication imperfections. The first one is based on electrostatic spring softening and tuning. The basic operation principle is first introduced. Then a full derivation of this method on a real MRIG configuration is conducted. Experimental results confirm that this compensation scheme can significantly attenuate the parameter mismatch.

The other compensation scheme considered in this dissertation is an adaptive compensation scheme consisting of three feedforward controllers. Each of them runs on top of the corresponding feedback control loop and estimates and compensates parameter mismatches in real time. We also present a stability and convergence analysis that shows such adaptive controllers converge to the correct values and perfectly cancel the parameter mismatch. A simulation study performed on a MRIG model also confirms the efficacy of the compensation scheme. Then a self-calibration process is proposed to automatically calibrate the gyroscope. This self-calibration method requires no human involvement or auxiliary device, hence enables the gyroscope to calibrate itself whenever necessary, even in use.